Impulsive Systems Triggered by Superposed Renewal Processes
Source: University of California
The authors consider impulsive systems with several reset maps triggered by independent renewal processes, i.e., the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals. Considering linear dynamic and reset maps, they establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one. The result builds upon a stochastic Lyapunov function approach which allows for providing stability conditions in the general case where the dynamic and the reset maps are non-linear.